No, you can't do a BAMS and an MSc degree together, but you can pursue an MSc program after completing your BAMS degree since both are degree courses you cannot do degree courses simultaneously.After completion of BAMS ,you will be a complete docter, you can get job with officer grade, or you can do Post graduation, or you can do your own clinic, you will be better than M Sc in all aspects, but both are diffrent,it depends on your choice and interest.

Dont get distracted by multiple options go with the career which align with your future goals.further, ssc cgl is different from your career options like bams and msc it includes maths, reasoning, english, current affairs which is not easy to crack.